Mix first 5 ingredients in small bowl; cover gremolata and set aside. Heat heavy large skillet over medium-high heat. Add saffron and stir until slightly darker, about 30 seconds. Transfer to another small bowl; cool and crumble saffron. DO AHEAD: Gremolata and saffron can be made 2 hours ahead. Let stand at room temperature.

Sprinkle chicken lightly with coarse salt and pepper. Heat 1 tablespoon oil in heavy large skillet over medium-high heat. Working in batches and adding more oil as needed, cook chicken until lightly browned and just cooked through, about 2 minutes per side. Arrange chicken on platter; tent with foil.

Add 1 tablespoon oil and butter to same skillet. Add white and green parts of onions and sauté until beginning to soften, about 4 minutes. Add asparagus. Sprinkle saffron over vegetables. Sprinkle with coarse salt and pepper and sauté 1 minute. Add broth, reduce heat to medium, and simmer uncovered until vegetables are tender and broth reduces and thickens to glaze, about 5 minutes. Stir in crème fraîche and gremolata. Season with salt and pepper. Using slotted spoon, transfer vegetables to platter, arranging around chicken. Drizzle sauce over chicken and serve.